Next: Exercises Up: Elementary Statistical Operations Previous: Elementary Statistical Operations

## First Steps

Statistical data usually consists of groups of numbers. Devore and Peck [11, Exercise 2.11,] describe an experiment in which 22 consumers reported the number of times they had purchased a product during the previous 48 week period. The results are given as a table:

To examine this data in XLISP-STAT we represent it as a list of numbers using the list  function:

```> (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8)
(0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8)
>
```
Note that the numbers are separated by white space (spaces, tabs or even returns), not commas.

The mean  function can be used to compute the average of a list of numbers. We can combine it with the list function to find the average number of purchases for our sample:

```> (mean (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8))
3.227273
>
```
The median  of these numbers can be computed as
```> (median (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8))
2
>
```

It is of course a nuisance to have to type in the list of 22 numbers every time we want to compute a statistic for the sample. To avoid having to do this I will give this list a name using the def  special form :

```> (def purchases (list 0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8))
PURCHASES
>
```
Now the symbol purchases has a value   associated with it: Its value is our list of 22 numbers. If you give the symbol purchases to the evaluator then it will find the value of this symbol and return that value:
```> purchases
(0 2 5 0 3 1 8 0 3 1 1 9 2 4 0 2 9 3 0 1 9 8)
>
```
We can now easily compute various numerical descriptive statistics for this data set:
```> (mean purchases)
3.227273
> (median purchases)
2
> (standard-deviation purchases)
3.279544
> (interquartile-range purchases)
3.5
>
```

XLISP-STAT also supports elementwise arithmetic  operations on lists of numbers. For example, we can add 1 to each of the purchases:

```> (+ 1 purchases)
(1 3 6 1 4 2 9 1 4 2 2 10 3 5 1 3 10 4 1 2 10 9)
>
```
and after adding 1 we can compute the natural logarithms of the results:
```> (log (+ 1 purchases))
(0 1.098612 1.791759 0 1.386294 0.6931472 2.197225 0 1.386294 0.6931472
0.6931472 2.302585 1.098612 1.609438 0 1.098612 2.302585 1.386294 0
0.6931472 2.302585 2.197225)
>
```

Luke Tierney
Tue Jan 21 15:04:48 CST 1997